Question

modeling real life use the diagram and the steps below to prove that the distance from the restaurant to the movie theater is the same as the distance from the cafe to the dry cleaners. let ( r ) represent the restaurant, ( s ) represent the shoe store, ( m ) represent the movie theater, ( c ) represent the café, ( f ) represent the florist, and ( d ) represent the dry cleaners. a. identify what is given and what is to be proven for the situation. b. write a two - column proof. statements 1. 2. 3. 4. 5. reasons 1. given 2. segment addition postulate 3. segment addition postulate 4. substitution property of equality 5. substitution property of equality

Explanation:

Step1: Identify given and to - prove

Given: \(RS = CF\), \(SM=MC = FD\). To prove: \(RM = CD\)

Step2: Use Segment Addition Postulate for \(RM\)

By Segment Addition Postulate, \(RM=RS + SM\)

Step3: Use Segment Addition Postulate for \(CD\)

By Segment Addition Postulate, \(CD=CF + FD\)

Step4: Substitute \(RS\) with \(CF\)

Since \(RS = CF\), we can substitute in the expression for \(RM\) (but we'll do a full substitution in the next step)

Step5: Substitute \(RS\) with \(CF\) and \(SM\) with \(FD\)

Substitute \(RS = CF\) and \(SM = FD\) into \(RM=RS + SM\). Then \(RM=CF + FD\). Since \(CD=CF + FD\) (from Step 3), by substitution property of equality, \(RM = CD\)

Answer:

1. \(RS = CF\)
2. \(RM=RS + SM\)
3. \(CD=CF + FD\)
4. \(RM=CF + SM\) (after substituting \(RS\) with \(CF\) in \(RM = RS+SM\))
5. \(RM = CD\) (after substituting \(SM\) with \(FD\) in \(RM=CF + SM\) since \(SM = FD\))